Estimation of the smallest eigenvalue of an nth-order linear boundary value problem

被引：3
|
作者：
Almenar, Pedro [1 ]
Jodar, Lucas [2 ]
机构：
[1] Vodafone Spain, Grp Networks, Avda Amer 115, Madrid 28042, Spain
[2] Univ Politecn Valencia, Inst Univ Matemat Multidisciplinar, Valencia, Spain
来源：
MATHEMATICAL METHODS IN THE APPLIED SCIENCES | 2021年 / 44卷 / 06期
关键词：
cone theory; eigenvalue; Green function; invariant subspace; Lyapunov inequality; nth‐ order linear boundary value problem; operator norm; POSITIVE SOLUTIONS; POINTS;
D O I：
10.1002/mma.7047
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
This paper describes a recursive procedure to estimate the smallest eigenvalue of an nth-order boundary value problem under a wide set of boundary conditions. The procedure yields lower and upper bounds for that eigenvalue as well as an estimation of the associated eigenfunction, both of which are shown to converge to their exact values as the recursion index grows. A simpler version of the procedure is also displayed for the self-adjoint case.
引用
收藏
页码：4491 / 4514
页数：24
相关论文
共 50 条
  • [1] Boundary value problem for an nth-order operator equation
    A. Ya. Lepin
    L. A. Lepin
    V. D. Ponomarev
    [J]. Differential Equations, 2010, 46 : 452 - 454
  • [2] Boundary value problem for an nth-order operator equation
    Lepin, A. Ya.
    Lepin, L. A.
    Ponomarev, V. D.
    [J]. DIFFERENTIAL EQUATIONS, 2010, 46 (03) : 452 - 454
  • [3] Fuzzy initial value problem for Nth-order linear differential equations
    Buckley, JJ
    Feuring, T
    [J]. FUZZY SETS AND SYSTEMS, 2001, 121 (02) : 247 - 255
  • [4] On boundary value problems for an nth-order equation
    N. I. Vasil’ev
    A. Ya. Lepin
    L. A. Lepin
    [J]. Differential Equations, 2010, 46 : 182 - 186
  • [5] On boundary value problems for an nth-order equation
    Vasil'ev, N. I.
    Lepin, A. Ya.
    Lepin, L. A.
    [J]. DIFFERENTIAL EQUATIONS, 2010, 46 (02) : 182 - 186
  • [6] The principal eigenvalue of some nth order linear boundary value problems
    Pedro Almenar
    Lucas Jódar
    [J]. Boundary Value Problems, 2021
  • [7] EXISTENCE OF SOLUTION TO A BOUNDARY VALUE PROBLEM FOR AN ORDINARY NON-LINEAR NTH-ORDER DIFFERENTIAL EQUATION
    LEPIN, AY
    MYSHKIS, AD
    [J]. DOKLADY AKADEMII NAUK SSSR, 1966, 169 (01): : 16 - &
  • [8] The principal eigenvalue of some nth order linear boundary value problems
    Almenar, Pedro
    Jodar, Lucas
    [J]. BOUNDARY VALUE PROBLEMS, 2021, 2021 (01):
  • [9] Improving Results on Solvability of a Class of nth-Order Linear Boundary Value Problems
    Almenar, Pedro
    Jodar, Lucas
    [J]. INTERNATIONAL JOURNAL OF DIFFERENTIAL EQUATIONS, 2016, 2016
  • [10] Existence of positive solutions for nth-order boundary value problem with sign changing nonlinearity
    Xie, Dapeng
    Bai, Chuanzhi
    Liu, Yang
    Wang, Chunli
    [J]. ELECTRONIC JOURNAL OF QUALITATIVE THEORY OF DIFFERENTIAL EQUATIONS, 2008, (08) : 1 - 10
12345